In most cases, your host will handle it...
However if you have a VPS or dedicated server, you have access to an enhanced Cpanel-type interface called WHM. For my VPS, WHM contains a link to configure the firewall
, and that's where banned IP addresses are listed.
In Cpanel you have the option to ban IP addresses yourself, but there is no "un-ban" for the IPs that tripped mod-security, so you need to speak with your host. This is one of the limitations of shared hosting
It's difficult to trouble-shoot this problem - Google comes in a with an assorted range of IP addresses, so it's not easy to pin down. If you can isolate the day, your host may be able to find the IP that got banned.
Moving the DNS should fix the problem, but that's an extreme measure. I was panicked in other thread as it wasn't my own site (a shared project)... the next time it happened to one of my own sites, I found the IP address in the banned list.
Hope this helps!